n1 is the smallest whole number for which this inequality works :

(1+x)^n >1 +n*x + n*x^2

also i am given that x>0

find n1

and prove this inequality for every n=>n1 by induction.

the base case:

(1+x)^n1 >1+n1*x + n1*x^2

i think its correct because i was told that this inequality works for n1.

n=k step we presume that this equation is true :

equation 1: (1+x)^k >1 +k*x + k*x^2

n=k+1 step we need to prove this equation:

equation 2: (1+x)^(k+1) >1 +(k+1)*x + (k+1)*x^2

now i need to multiply equation1 by sum thing

and

do

if a<b<c

then a<c

how to do thing in this case?